I would argue that local values played a part, but an emphasis on education, long term planning, and a lack of US political dysfunction were much more impactful.
Also worth mentioning that the wins over Japan and Germany weee pretty decisive. 1960s South Vietnam, 2001 Afghanistan, and 2003 Iraq (and potentially 1991 Russia) were all pretty ham fisted efforts and there was no US consensus about what to do with the country.
I don’t know enough about 1951 S Korea to say anything useful, except it was a military autocracy until the 1980s, at which point it made an incredible shift towards democracy and the economic growth story was one of the world’s most amazing.
The economic growth, or at least the seeds thereof, largely came during Park Chung Hee's dictatorship, which ended in 1979 with his assassination. GDP per capita increased over tenfold during his tenure. The shift towards democracy afterwards was tumultuous for a while, with the first real civilian presidency being Kim Young-sam's in the 90s.
You're definitely right that the growth story is one of the most amazing in history. It's a country roughly the size of Indiana with no natural resources to speak of, and over 50 million people (over 10 million more than California, the most populous state) crammed into the few flatlands it has, being a very mountainous country. Yet it was able to go from an agrarian society to a highly developed nation, with the 12th largest GDP, home to feats like building a third of the world's tonnage of ships. It's absolutely wild.
The Marshall Plan.
And people forget that it had quite a lot of opposition back at home in the US.